Cancellation of simple optical anisotropies without use of a Faraday mirror

We first derive the round-trip Jones matrix for double passage through a reciprocal optical medium by means of reflection off a plane mirror that could be optically anisotropic. We then show that if a medium with only linear birefringence and linear dichroism is placed between a pair of orthogonal quarter-wave plates with principal axes at 45 degrees to that of the medium and the sandwich is placed in front of an isotropic mirror it behaves, under double passage, like an isotropic medium. We describe a simple liquid crystal device that behaves, in reflection, as an isotropic medium whose refractive index can be varied by application of an electric field, thus acting as a phase only modulator for light in any polarization state.